I'll be staying at an Inn in Whitchutch (without a car) and really want to get out to Highclere and or Watership Down area. Uber doesn't serve this town and hisses don't go into that countryside specifically. Any tips for finding a ride?
Trains are useful for connecting major towns, but not rural areas. Getting from Whitchurch to either of these places is difficult without a car. Try rome2rio.com which will show your options. The journey to Highclere will take over 1.5 hours by public transport for a direct journey of just a few miles.
Catching a taxi is likely to be your best bet - the inn where you are staying should be able to recommend a company.